Example 3.2 Using a Grünbaum's style approach [1]}, we search for operators of order 4 in \(A_1({\bf C})\)  that commute with a nontrivial operator (not in \({\bf C}[L_4]\) ) of order 10. We fix
\(L_4=\big (\partial ^2+x^4+1\big )^2+U(x)\partial +W(x),\) 
